Theorems · Theorem · order theory
ClosureOperator.closure_sup_closure_left
∀ {α : Type u_1} [inst : SemilatticeSup α] (c : ClosureOperator α) (x y : α), c (c x ⊔ y) = c (x ⊔ y)- Defined in
- Mathlib.Order.Closure
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- SemilatticeSup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- LE.le.transproof · cited by 3,151
- le_antisymmproof · cited by 2,068
- le_reflproof · cited by 2,061
- SemilatticeSupstatement and proof · cited by 785
- le_imp_le_of_le_of_leproof · cited by 576
- ClosureOperatorstatement and proof · cited by 371
- le_sup_leftproof · cited by 265
- le_sup_rightproof · cited by 242
- sup_leproof · cited by 159
- sup_le_supproof · cited by 48
- ClosureOperator.le_closureproof · cited by 19
Cited by5
Results whose statement or proof uses this declaration.
- ClosureOperator.closure_sup_closure_rightproof · cited by 4
- convexHull_convexHull_union_leftproof · cited by 1
- ClosureOperator.closure_sup_closureproof · cited by 1
- LowerAdjoint.closure_sup_closure_leftproof · cited by 1
- Convexity.convexHull_convexHull_unionproof · cited by 0